1Dept. of Mathematics, American University of Beirut, c/o New York Office, 850 Third Ave. 18th floor, New York, NY 10022-6297, U.S.A. 2Let H be an algebraic subgroup of a linear algebraic group G over an algebraically closed field K. We show that H is observable in G if and only if there exists a finite-dimensional rational G-module V and an element v of V such that H is the isotropy subgroup of v as well as the isotropy subgroup of the line Kv. Moreover, we give a similar result in the case where H contains a normal algebraic subgroup A which is observable in G. In this case, we deduce that H is observable in G whenever H/A has non non-trivial rational characters. We also give an example from complex analytic groups. 3[
Journal of Lie Theory, Tome 12 (2002) no. 1, pp. 301-304
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Nazih Nahlus. A Note on Observable Subgroups of Linear Algebraic Groups and a Theorem of Chevalley. Journal of Lie Theory, Tome 12 (2002) no. 1, pp. 301-304. http://geodesic.mathdoc.fr/item/JOLT_2002_12_1_a15/
@article{JOLT_2002_12_1_a15,
author = {Nazih Nahlus},
title = {A {Note} on {Observable} {Subgroups} of {Linear} {Algebraic} {Groups} and a {Theorem} of {Chevalley}},
journal = {Journal of Lie Theory},
pages = {301--304},
year = {2002},
volume = {12},
number = {1},
url = {http://geodesic.mathdoc.fr/item/JOLT_2002_12_1_a15/}
}
TY - JOUR
AU - Nazih Nahlus
TI - A Note on Observable Subgroups of Linear Algebraic Groups and a Theorem of Chevalley
JO - Journal of Lie Theory
PY - 2002
SP - 301
EP - 304
VL - 12
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UR - http://geodesic.mathdoc.fr/item/JOLT_2002_12_1_a15/
ID - JOLT_2002_12_1_a15
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%A Nazih Nahlus
%T A Note on Observable Subgroups of Linear Algebraic Groups and a Theorem of Chevalley
%J Journal of Lie Theory
%D 2002
%P 301-304
%V 12
%N 1
%U http://geodesic.mathdoc.fr/item/JOLT_2002_12_1_a15/
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Let H be an algebraic subgroup of a linear algebraic group G over an algebraically closed field K. We show that H is observable in G if and only if there exists a finite-dimensional rational G-module V and an element v of V such that H is the isotropy subgroup of v as well as the isotropy subgroup of the line Kv. Moreover, we give a similar result in the case where H contains a normal algebraic subgroup A which is observable in G. In this case, we deduce that H is observable in G whenever H/A has non non-trivial rational characters. We also give an example from complex analytic groups.
